I joined the department of Applied Math in fall 2014. Previously I was a Herman Goldstine Postdoctoral fellow in Mathematical Sciences at IBM Research in Yorktown Heights, NY, and a postdoctoral fellow via the Fondation Sciences Mathématiques de Paris at Paris 6 (JLL lab), after doing my doctoral work at Caltech.
Broadly speaking, our group is interested in information extraction from various types of datasets. We are part of a hybrid field combining applied math with computer science and signal processing techniques. Some specific topics we research are:
- Optimization: first-order methods, quasi-Newton methods, primal-dual algorithms, convex analysis.
- Types of problems: from computational imaging, and semi-definite programs (from relaxations, or from robust PCA)
- Mathematical applications: compressed sensing and variants, matrix completion and variants (robust PCA…), non-negative matrix factorization and end-member detection, sparse SVM
- Numerical linear algebra: randomization and its interplay with optimization methods
- Sampling theory: how to make the best use of your resources when confronted with big data
- Physical applications: radar ADC using compressed sensing, quantum tomography, MRI, medical imaging, IMRT, renewable energy, big-data
- Recent applications (2015--2018) have been in super-resolution (optical) microscopy and photo-acoustic microscopy
To get a more specific idea of the research our group does, here are some topics we're doing in 2018:
- Parametric and compressive estimation, for phase retrieval (Jessica) in x-ray imaging, and for discovering archaeological ruins (Abby) in radar imaging without creating a DEM
- Theoretical machine learning: sub-sampling and sketching (Farhad, Eric)
- Avoiding/analyzing saddle points in non-convex optimization: for biconvex programming in program analysis and/or controls (Jessica), and for dictionary learning and neural network learning (Leo)
- Improving accuracy of sparse estimation using mixed-integer programming (Eric, Leo)
- Efficient computation of the cross-ambiguity function (CAF) for signal processing, to estimate time-of-arrival of radar signals (James)
- Randomized algorithms for numerical linear algebra and optimization (James, Derek)
- Optimization algorithms in general, and ill-conditioning and pre-conditioning (James, Jessica, Osman)
- Efficient algorithms for GPUs (James, Derek, Jessica)
- Tensor decompositions (Osman, Derek)
- Robust estimation (Richie)
- Misc imaging applications (for optical super-resolution, with Carol Cogswell's group in ECEE; and for photo-acoustic super-resolution, with Todd Murray's group in Mech E)
- Stochastic variance reduction methods for non-linear inverse problems
- Remote sensing of the Chesapeake bay (Cheryl)
- Behavior genetics (Richard, Farhad)
Our research group website has more information on research topics.
(note: there is also some interesting description of our work at our old website. The only website that we update regularly is the research group website)
January 2018, I am one of four founding members of the new Imaging Science center in the engineering college. Here is the new Imaging Science IRT website.
You may be interested in joining the Colorado data science team.
We run a Statistics, Optimization and Machine Learning seminar (Fall 2017, this is usually 3:30 Tuesdays at Newton lab). Anyone is welcome to show up.
(to receive announcements about talks at the seminar, please sign up for the StatOptML google group).
For K-12 students and educators interested in partnering with CU
Thinking about a PhD in Applied Math at CU?
- CU Boulder is a top-25 research university with excellent resources
- According to NSF data, CU is #13 nationwide in total federal obligations, #7 nationwide by number of full-time graduate students in science, engineering, and health, and if you combine with our medical school, we are #20 nationwide in total R&D expenditures (other top-10 schools in R&D, like Duke, are already combined with their medical schools).
- CU is ranked the #2 university in the world for geosciences by the US News and World Report
- #11 internationally in computer science by normalized citation index, #35 overall internationally in physics, etc.
- From the aerospace department website, CU is the #1 public university for NASA research funds, Colorado is the 2nd largest aerospace economy in the US, and our aerospace program is ranked #8 (graduate) and #10 (undergraduate)
- A unique feature of CU is the strength of our 11 institutes (ATLAS, Biofrontiers, CIRES, INSTAAR, IBS, ICS, JILA, LASP, ... ), as well as the nearby national labs (NOAA, NIST, NCAR)
- Applied Math is at the center of quantitative work in the institutes, as well as new statistical efforts on campus
- We are one of just a handful of specialized Applied Math departments in the US. An applied math degree greatly distinguishes graduates
- Ready to apply? Please apply to our department (we do not do direct admission into a research group)
Thinking about applied math in general?